Related papers: Hybridized CutFEM for Elliptic Interface Problems
We consider the discretization of a stationary Stokes interface problem in a velocity-pressure formulation. The interface is described implicitly as the zero level of a scalar function as it is common in level set based methods. Hence, the…
This paper deals with the local recovery of conservative fluxes for an elliptic interface problem with discontinuous coefficients. The transmission conditions on the interface are imposed weakly and the discretisation is achieved by using…
We develop a method for solving elliptic partial differential equations on surfaces described by CAD patches that may have gaps/overlaps. The method is based on hybridization using a three-dimensional mesh that covers the gap/overlap…
In this article, we develop and analyze a finite element method with the first family N\'ed\'elec elements of the lowest degree for solving a Maxwell interface problem modeled by a $\mathbf{H}(\text{curl})$-elliptic equation on unfitted…
We propose a low-dimensional interface reduction method for elliptic interface problems based on conservative flux reconstruction. The approach combines a fitted $P_1$ finite element discretization with a flux recovery procedure following…
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
This article presents and analyzes a $p^{th}$-degree immersed finite element (IFE) method for elliptic interface problems with nonhomogeneous jump conditions. In this method, jump conditions are approximated optimally by basic IFE and…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
We study finite element approximations of elliptic and parabolic interface problems with discontinuous coefficients and nonlinear jump conditions. We introduce a scalar interface reduction in which the solution is decomposed into a…
We develop a general framework for construction and analysis of discrete extension operators with application to unfitted finite element approximation of partial differential equations. In unfitted methods so called cut elements intersected…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
We consider a hybrid FEM-BEM method to compute approximations of full-space linear elliptic transmission problems. First, we derive a priori and a posteriori error estimates. Then, building on the latter, we present an adaptive algorithm…
We develop a conservative cut finite element method for an elliptic coupled bulk-interface problem. The method is based on a discontinuous Galerkin framework where stabilization is added in such a way that we retain conservation on macro…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
Accurately depicting multiphysics interactions in interfacial systems requires computational frameworks capable of reconciling geometric adaptability with strict conservation fidelity. However, traditional spatiotemporal discretisation…
In this paper, a stabilized extended finite element method is proposed for Stokes interface problems on unfitted triangulation elements which do not require the interface align with the triangulation. The velocity solution and pressure…
We present a unified framework for developing and analysing immersed finite element (IFE) spaces for solving typical elliptic interface problems with interface independent meshes. This framework allows us to construct a group of new IFE…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
We propose a new finite element method for Helmholtz equation in the situation where an acoustically permeable interface is embedded in the computational domain. A variant of Nitsche's method, different from the standard one, weakly…